[Mrtrix-discussion] FOD amplitude

[David Raffelt]

Hi James,
I've answered each of your questions below.
Cheers,
Dave



On 15 March 2013 23:20, James Cole <james.cole at ucl.ac.uk> wrote:

>  Hi Dave,
> Thanks very much for the detailed response, that's really very useful.
> I've responded to your points (with a few more questions) inline:
>
>
> On 15/03/13 03:59, David Raffelt wrote:
>
> Hi James,
> Just to clarify, do you mean you extract a single peak with the largest
> amplitude within each voxel? Then normalise by the max amplitude across all
> voxels and subjects? If so, one potential issue is that the largest peak in
> corresponding voxels across subjects is not guaranteed to belong to the
> same fibre bundle. Also, during pathology you might see a decrease in the
> FOD peaks of one fibre, such that they are no longer the dominant peak in
> that region (and therefore are excluded from your analysis).
>
> Yes, that's exactly what I did. I agree that the largest peaks in
> corresponding voxels between individuals may well not belong to the same
> fibre bundle, but I think you could argue that this is no worse than the
> 'averaging' of different fibre bundles inherent in the tensor model. At
> least this way you can claim to be actually measuring a discrete fibre
> bundle, rather than something potentially not aligned to any tracts, as may
> happen with the primary eigenvector in DTI.
> As I understand it the full AFD approach might help rectify this tract
> correspondence problem, as could some other methods for determining common
> orientations (e.g. FSL bedpostX). These are things I definitely would like
> to explore in the long term.
>
> I guess if you see any group differences in the largest peak you will need
to be careful about the interpretation and check that it is not due to a
miss match in peak correspondence. However, interpreting FA differences
requires the same level of care anyway.

>
>  Simulations suggest the AFD along a given direction is proportional to
> the intra-axonal volume of axons aligned with that direction (at least with
> high b-values and long gradient pulse durations). Using lower b-values
> means that the AFD is also dependent on the signal from hindered
> extra-axonal water. And therefore the interpretation of any AFD group
> differences is not as clear cut.
>
> Interesting to know. I'm generally a bit concerned about the low bvalue in
> my data, but keen to try and use some multi-fibre/non-tensor methods
> nonetheless, even if it's somewhat exploratory. One advantage with the
> sample I'm using (Huntington's Disease) is that there's strong post-mortem
> evidence that shows demyelination, loss of axonal density and number of
> axons - so even if the interpretation isn't straightforward, then group
> differences are still likely to be pathological.
>


You are right in that even if the interpretation isn't clear, these changes
would cause a decrease in the radial DW signal and therefore a decrease in
AFD.

>
>  The peak AFD amplitude is probably not a bad estimate of the total
> intra-axonal volume of axons belonging to the respective FOD lobe. However,
> inter-subject differences in fibre curvature (in subject space) will
> influence the peak (due to a difference in the spread of the FOD lobe).  A
> better measure would be to use the integral of each FOD lobe. Rob uses the
> integral for his SIFT method, and I'm presenting a new tractography-based
> statistical method that uses the AFD integral at ISMRM next month.
>
> Sounds great. I've had a read of the appendix and Algorithm 1 in Rob's
> SIFT paper and can definitely see the justification for using the integral,
> rather than the peak. As mention later, you're planning to implement this
> in MRtrix in the future, but in the meantime, do you have a script that
> runs the density sampling and calculates the integral that you can make
> available?
>

We don't currently have any commands that will output the integral per FOD
lobe for all voxels in the brain. This is something we could probably add
to the next major MRtrix release, however by that point we also hope to
release the AFD analysis tools, so you are better of using these instead of
comparing the largest FOD integral.

>
>
>  One other issue is related to transforming the AFD peak amplitudes into
> template space. Modulation needs to be applied when spatially normalising
> any DWI measure representative of the restricted intra-axonal water
> fraction of a specific fibre population  (whether it is the AFD peak,
> integral, or partial volume fractions computed using other methods, e.g.
> Behren's Ball and Stick model or Assaf's CHARMED). As discussed in the AFD
> paper, non-linear transformations may alter the width of a fibre bundle,
> and therefore modulation is needed to preserve the total intra-axonal
> volume of axons passing through any given cross-section of a fibre bundle.
>
> Again, modulation looks very sensible, I can see the problems that may
> arise if it's not done. Would you also happen to have a script available to
> do this in using the mrtrix framework?
>
>
Sorry we don't have anything currently. I have been slowly porting the FOD
registration, reorientation and modulation software to MRtrix, however when
this gets released will depend my spare time in the future.

>
>  Are you computing FODs using a single group-average response function
> for all subjects? To do AFD analysis you also must account for intensity
> variation across scans. Due to patient- and scan-specific scanner
> calibrations, the magnitude of the MR signal across different scans is not
> comparable. One way to account for this is to intensity normalise the DW
> images using some reference point. Ideally, the median CSF b=0 signal would
> be a good reference since it is unlikely to vary during pathology. However,
> at the current DWI resolution it is often hard to get a clean
> partial-volume-free estimate of the CSF, particularly in young patient
> groups. Alternatively you could use the median b=0 signal from brain
> parenchyma, however this is not ideal since it might be affected by the
> pathology being investigated.
> The other way to account for scan intensity variation is to perform CSD
> using a subject-specific response function, however this is less robust and
> you might reduce your power to detect AFD differences due to larger group
> variation, or the possibility of pathology affecting voxels used to
> estimate the response function.
>
> I used a subject-specific response function. Interestingly, the voxels
> that showed group differences were not those that were generally included
> in the single fibre mask used to estimate the response function. Not sure
> if this has any bearing the robustness of the calculation. I think I'll try
> and calculate the median CSF signal to intensity normalise the subjects,
> then use one response function across all.
>
>
If you have a pathology-induced AFD decrease within voxels of your single
fibre mask, then this might cause an artificial AFD increase to be detected
in other voxels outside the mask.  Using the CSF signal is the best option,
however you might want to use the 95th percentile instead of the median
since the majority of CSF containing voxels will contain other tissue as
well.

You might want check that the 95th percentile CSF intensities that you
estimate are not statistically different between your two groups. This is a
good sanity check to make sure that the normalisation is not going to be
biased by the pathology (for example one group might have less atrophy and
less robust CSF estimates than the other)

Finally, one thing I did not mention in the previous email, is that since
the AFD is proportional to the DWI signal you should perform some sort of
bias field correction. I currently use N4ITK to estimate the field on the
b=0 image, and apply this to correct all DW volumes.

>
>  Just to clarify, the max_amp metric represents the amount of diffusion
> in the peak direction only for diffusion orientation distributions dOFDs
> (i.e those computed by Q-ball and DSI). Whereas FODs model the intra-axonal
> volume of fibres as a function of orientation. The amplitude of so-called
> "model free" diffusion ODFs is less informative, since it is impossible to
> tease out the contribution from multiple underlying fibre populations
> without some type of model (which in the case of spherical deconvolution is
> the response function).
>
> OK, so hopefully that by using the FODs in my case, I'll be able to see
> something more biologically meaningful - even if I can't directly claim to
> be measuring diffusion.
>
>
>  Also, the peak FOD amplitude is more akin to the apparent* radial*diffusivity of the respective fibre population (and not the axial
> diffusivity as you suggest). Pathology-induced changes to restriction are
> more likely to influence the DW signal along radial orientations
> (especially at high b-values where the axial DW signal is non-existent). A
> decrease in the radial DW signal will present as a decrease in AFD along
> the fibre direction, and an increase in the radial diffusivity. Although I
> should warn against thinking of AFD in terms of radial diffusivity, since
> thinking in terms of diffusivity is clearly not a good way of looking at
> the DW signal arising from a *restricted* diffusion environment.
>
> Very interesting, thanks for the clarification. On reflection, I can see
> that this definitely makes more sense. In my experience, RD is more
> sensitive to pathology than AD, so if I can explain this metric to people
> as approximately analogous to RD, that might be more comprehensible.
> However, as you say, I'll be careful not to make any claims about
> diffusivity per se, given the restricted environment that the metric is
> derived from.
>
>
>
>  Since I'm on a roll, I might as well mention that TBSS is not ideal for
> doing 'whole brain' voxel-based analysis. Aside from the fact that it does
> not really analyse all brain voxels, projecting your measure of interest
> onto a skeleton based on the highest FA is problematic in crossing-fibre
> regions.
>
> I quite agree. I didn't actually use a TBSS skeleton for that very reason.
> I just used the randomise tool to run the GLM stats, and thought I'd
> mention TBSS as that's the context that most people are familiar with
> randomise from.
>
> Great.

>
>  In terms of doing AFD analysis in the future, we are hoping to release
> the tools as part of the next major MRtrix release, however this will
> depend on how much free time I have in the coming months.
>
>   Quite understandable! Thanks again for all the advice.
> James
>
>  Cheers,
> Dave
>
>
>
>
>
>
>
>
> ---------- Forwarded message ----------
> From: James Cole <james.cole at ucl.ac.uk>
> Date: 15 March 2013 04:28
> Subject: [Mrtrix-discussion] FOD amplitude
> To: mrtrix-discussion at www.nitrc.org
>
>
>  Dear MRtrixers,
> I've been using mrtrix for various things and came up with an approach
> that I wanted to run by the experts. It might be that I'm barking up
> entirely the wrong tree, so could use some guidance. Regarding voxelwise
> metrics derived from the spherical deconvolution (I saw the apparent fibre
> density (AFD) paper and this is something I'd be interested in trying in
> the long run), I wondered whether the largest FOD lobe might be sensitive
> to pathology. Here's my analysis:
>
> Having run CSD (Lmax = 6, the b-value is only 1000, 42 directions) on my
> data, I used find_SH_peaks, dir2amp and FSL's fslroi to extract the FOD of
> the largest amplitude (I called this max_amp) and thus was able to generate
> voxelwise max_amp maps per subject, in native space.
>
> I then normalised the max_amp maps (by dividing by 3.5, to give a scalar
> in the 0-1 range), having assessed the maximum amplitude in any voxel
> across all subjects (which was 3.51ish). The idea being that the the scalar
> now represents a score based on the amplitude of the FOD lobe relative to
> the highest possible amplitude in vivo tissue; thus 0 = absence of FOD and
> 1 = maximum possible FOD amplitude.
>
> These normalised max_amp maps were then warped into group space using the
> warps calculated from generating a groupwise template from FA maps. I then
> created a mask using a threshold of FA>0.2 (to limit analysis to white
> matter) and finally ran some stats (using FSL randomise as per TBSS). In a
> group of 10 controls and 15 patients there were a number of significant
> clusters of increased max_amp in controls, roughly corresponding to the
> corticospinal tract and corona radiata. There were no increases in
> patients.
>
> The rationale behind this comes from the idea that the max_amp metric
> represents the amount of diffusion in the principle direction, but
> uncontaminated by crossing fibre effects (so perhaps a 'better' version of
> axial diffusivity, I suppose). I'm not assuming this idea is original by
> any means, perhaps just the implementation of it in mrtrix.
>
> Apologies for the long post, but I'd be really appreciative of some expert
> opinions. Any ideas for theoretical / practical improvements, or reasons
> why this might not be representing what I think it is would be most helpful.
>
> Many thanks,
> James
>
> --
> *James Cole PhD | Research Associate | Huntington's Disease Research
> Group | UCL Institute of Neurology*
>
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>
>
>
>  --
>  *David Raffelt (PhD)*
> Post Doctoral Fellow
>
>  The Florey Institute of Neuroscience and Mental Health
> Melbourne Brain Centre - Austin Campus
> 245 Burgundy Street
> Heidelberg Vic 3084
> Ph: +61 3 9035 7024
>  www.florey.edu.au
>
>
>


-- 
*David Raffelt (PhD)*
Post Doctoral Fellow

The Florey Institute of Neuroscience and Mental Health
Melbourne Brain Centre - Austin Campus
245 Burgundy Street
Heidelberg Vic 3084
Ph: +61 3 9035 7024
www.florey.edu.au
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